House Republicans quickly sloughed off the shock of Majority Leader Eric Cantor's defeat and were immediately thrust into a weeklong, all-out sprint for power.

Next Thursday's vote for new leadership will have ripple effects that touch every aspect of House policymaking, messaging and scheduling.

Republicans are hoping for a quick transition, counting on the chaos of this week’s unexpected primary results to give way to unity and a new leadership team. Speaker John A. Boehner of Ohio called on his conference to come together , even as internal elections are sure to tear them apart for the next week.

“This is the time for unity; the time for focus — focus on the thing we all know to be true: The failure of Barack Obama's policies and our obligation to show the American people we offer them not just a viable alternative, but a better future,” he told his conference in a private meeting Wednesday night. The conference was hastily called to see off Cantor. He will resign his leadership post on July 31, after suffering a crushing primary defeat in his Virginia district. He endorsed as his successor Majority Whip Kevin McCarthy of California, the third-ranking House Republican, whose operation is already in full swing.

McCarthy will field a challenge from a Texas Republican, although at press time it was unclear which one. Rules Chairman Pete Sessions announced his candidacy earlier in the day, but said that if conservative heavyweight Jeb Hensarling, the Financial Services chairman, enters the race, he may pull out. Hensarling is "prayerfully" considering it.

Either congressman will face a formidable foe in McCarthy.

McCarthy and about 30 of his allies huddled privately Wednesday afternoon, resolving to fan out and round up support, much like they do in the whip operation he heads. The group included members from McCarthy's whip team, as well as powerful panel heads such as Appropriations Chairman Harold Rogers of Kentucky, Ways and Means Chairman Dave Camp of Michigan and Energy and Commerce Chairman Fred Upton of Michigan.

"We’re trying to figure out who we need to talk to for Kevin," said Rep. Tom Rooney, R-Fla., a top McCarthy lieutenant. "We were talking about trying to put this to bed early."

The closed-door, secret ballot leadership election will be held on June 19, a fact that McCarthy’s allies believe benefits their candidate. They already have people working the phones and buttonholing members to round up votes, while other candidates would have to put a team together.

However, geography and ideology are working against McCarthy. There is a fervent desire among self-described conservative members to install one of their own in leadership, especially someone from a Southern state who is aligned more with the tea party movement and outside conservative groups.

Texas Republicans, who make up the largest GOP state delegation, are pining to elect one of their own to the top echelon of leadership. As Lone Star State Rep. Michael C. Burgess put it: “I’m always for the Texan.”

Hensarling can attract votes from both of those constituencies, potentially putting together a formidable voting bloc.

He is also close with Budget Chairman Paul D. Ryan of Wisconsin and Vice Chairman Tom Price of Georgia, influential members who can put together a solid whip operation. (Ryan, who is expected to take the Ways and Means gavel next year, said he is not interested in a leadership post, while Price said Wednesday he's considering a bid.)

Hensarling was attracting votes before he had even announced. A group of conservative members met throughout the day to game out their moves. Rep. Mick Mulvaney of South Carolina, one of those members, said Hensarling is his dream candidate for the position.

"I do think there's a difference between a red-state Republican and a blue-state or purple-state Republican. The people you go home to are different, the language that’s used is different,” said Mulvaney, who is running to head the conservative Republican Study Committee next year.

Rep. Mo Brooks of Alabama said McCarthy is not conservative enough for his taste; he’d prefer Hensarling.

Texas Republicans held their own meeting Wednesday, after the conference gathered, although there didn't appear to be a final resolution. Sessions said after the meeting he was still in the running and Hensarling said he hadn't made a decision and would not make any further announcements Wednesday.

Sessions said the delegation is giving him and Hensarling a chance to talk about who should run.

"I think that we need a chance to come together, talk about where we are and what we're doing," he said.

It is possible that only one vote could take place during next week's organization meeting. If McCarthy does lose, he can retain his position as majority whip. If he wins, another election will be held to fill his leadership slot.

In that race, Chief Deputy Whip Peter Roskam of Illinois is going head-to-head with RSC Chairman Steve Scalise of Louisiana.

In fact, the strength of McCarthy’s candidacy could be Roskam's greatest weakness, a cruel coincidence for two men who have worked closely together for the past several years.

Roskam has been working to build support for weeks on Capitol Hill and K Street, with meetings and financial donations to colleagues. One member said he is invited at least once a week to a dinner discussing his candidacy.

But if McCarthy wins, there may be even more of a desire among conservatives to vote against the Midwesterner and in favor of the Southerner.

Still, as some conservatives are pining for a red-state Republican to represent them at the leadership table, other moderate and blue-state Republicans said the current leadership team has done an effective job.

Rep. Pat Tiberi of Ohio said he has not decided whom to support, but said both McCarthy and Roskam are popular, despite coming from Democratic-leaning states.

“They both have a very successful tenure in their positions in leadership and they have a lot of support within the conference generally speaking for the job that they’ve done,” he said.

The rest of the leadership table looks to remain in place, at least through the November elections.

Rep. Cathy McMorris Rodgers of Washington announced that she would stay put as conference chairwoman. Conference Vice Chairwoman Lynn Jenkins of Kansas may have eyed McMorris Rodgers’ spot if it was vacant, but will remain in her post.

Interestingly, the one man whose future had been the most in question now seems the most stable. Boehner, whose next move was subject to rampant speculation, may be more inclined to remain speaker next year in order to avoid a leadership vacuum that could throw the conference into turmoil, aides and members said.